Quasicrystals with 1-D Translational Periodicity and a Ten-Fold Rotation Axis
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QUASICRYSTALS WITH 1-D TRANSLATIONAL PERIODICITY AND A TEN-FOLD ROTATION AXIS L. BENDERSKY Center for Materials Research, The Johns Hopkins University, Baltimore, MD and Institute for Materials Science and Engineering, National Bureau of Standards, Gaithersburg, MD ABSTRACT Studies of phase formation in rapidly solidified Al-Mn alloys (composition range 18-22 at% Mn) show that an icosahedral phase is replaced by another noncrystallographic phase, a decagonal phase. The decagonal phase is another example of quasicrystal: It has a noncrystallographic point group (10/m or lO/mmm) together with long-range orientational order and onedimensional translational symmetry. The decagonal phase is an intermediate phase between an icosahedral phase and a crystal both from the symmetry and from the solidification condition points of view. INTRODUCTION Last year the discovery of an icosahedral Al-Mn phase, which diffracts electrons like a single crystal but has non-crystallographic point group symmetry m35, was announced by Shechtman et al [1]. The icosahedral symmetry is inconsistent with translational periodicity yet the diffraction peaks are sharp. This contradiction can be resolved assuming a structure with quasiperiodic or almost periodic properties. A fourier transform (diffraction pattern) of a quasiperiodic or almost periodic function yields a continuum of true delta functions (Bragg peaks) [2,3]. For a quasiperiodic structure, or quasicrystal, any point symmetry is permitted for the diffraction pattern. The diffraction properties of the icosahedral phase can be successfully described using the concept of quasiperiodicity. Experimental diffraction patterns and high-resolution images [3,4,5] are in a good agreement with computer simulations, when an icosahedral quasilattice obtained by the Cut and Projection Method [6-8] was used as a model. At the same time, the conventional crystallographic explanation (multiple twinning, large unit cell [9-11]) is unable to explain all existing experimental evidence. It seems that icosahedral phase is a truly quasiperiodic solid. But what about the possibility for an infinite number of non-crystallographic point groups to exist? Recently, two other quasicrystals exhibiting non-crystallographic point groups different from m35 were reported: dodecagonal in the Ni-Cr system [12] and decagonal Al-Mn [13-15]. In this paper I present some details concerning the formation, stability and crystallography of the decagonal phase (also called T-phase). The relationship of this phase to the icosahedral phase is also discussed. FORMATION The conditions for decagonal phase formation were outlined in the paper by Schaefer et al [16]. The phase was observed in rapidly solidified Al-Mn alloys, in some other aluminum-transition metals alloys [17], in ternary AlMn-Ge and Al-Mn-Zn [18]. In this paper only the binary Al-Mn will be discussed. In melt-spun ribbons the decagonal phase starts to appear when the alloy composition is higher than -27 wt% Mn, growing epitaxially on the icosahedral phase dendrites, a
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